Answer:
3x^2-8x-3y
Step-by-step explanation:
combine like turms and rearrange
Take the sequence in 1a
The 10th term is 31
The 20th is 61
If you wanted to find these by continuing the series, you'd have to add 3 to the last number in the series, then 3 more, then 3 more, until you reach the 20th term. By this point, you will have added 3 to the first term 19 times. That's where the formula comes from. So here,
a = 4, the first term
n = 20, the number of the term we need
d = 3, how much we're adding each time between one term and the next
Then, to get the 20th term,
4 + (20 - 1) • 3 = 4 + (19 • 3) = 4 + 57 = 61
Answers
The 10th and 20th terms of each sequences are
a. 31; 61
b. 48; 98
c. 47; 97
(in <em>c</em>, you're adding the same <em>d</em> as in the sequence above, but your first term is one unit less)
d. -25; -75
(same thing as before, but now, <em>d</em> is negative)
e. 11.5; 16.5
(with <em>d</em>=1/2 or 0.5)
f. 6+1/2; 8+1/2
Use these to check your answers after applying the formula, but know that I calculated on the fly and didn't check these.
Answer:
1.2%
Step-by-step explanation:
We know that for every 500 computers, 6 are defective. So, to know what percentage of computers are defective on average, we can do a rule of three:
500 computers -> 6 defective
100 computers -> X defective
500/100 = 6/X
X = 100 * 6 / 500 = 1.2
So, in average, for every 100 computers, 1.2 are defective, so the percentage is 1.2% (1.2 for every 100)
X=length
y=width
Area (rectangle)=length x width
we suggest this system of equations:
y=x/5
xy=9/20
solve this system of equations by substitution method:
x(x/5)=9/20
x²/5=9/20
Least common multiple=20
4x²=9
x²=9/4
x=⁺₋√(9/4)
we have two solutions:
x₁=-3/2 it does not validate
x₂=3/2 ⇒y=x/5=(3/2)/5=3/10
The dimensions of the lake are:
lengh=3/2 miles
width=3/10 miles
to check:
Area=3/2 miles x 3/10 miles=9/20 miles².
width is 1/5 the length of the lake ⇒ 3/10 miles=(3/2) /5 miles
